Characterizations of recognizable picture series

Ina Mäurer
2007 Theoretical Computer Science  
The theory of two-dimensional languages as a generalization of formal string languages was motivated by problems arising from image processing and pattern recognition, and also concerns models of parallel computing. Here we investigate power series on pictures. These are functions that map pictures to elements of a semiring and provide an extension of two-dimensional languages to a quantitative setting. We assign weights to different devices, ranging from picture automata to tiling systems. We
more » ... ill prove that, for commutative semirings, the behaviours of weighted picture automata are precisely alphabetic projections of series defined in terms of rational operations, and also coincide with the families of series characterized by weighted tiling or weighted domino systems.
doi:10.1016/j.tcs.2007.01.019 fatcat:wopdjrx7wbcefiamcdr2opra4m